These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of c...

Persistence is considered in one-dimensional diffusion-limited cluster-cluster aggregation when the diffusion coefficient of a cluster depends on its size s as D(s) approximately s(gamma). The probabilities that a site has been either empty or covered by a cluster all the time define the empty and filled site persistences. The cluster persistence gives the probability of a cluster remaining int...

In spite of the promise of new techniques for constraining the mass distribution in galaxy clusters, much remains to be learned from galaxy orbital velocities. This article reviews the theory of potential estimation in hot dynamical systems like galaxy clusters. An analysis is presented of the Coma cluster, based on a sample of 1500 galaxies with probable membership, of which 450 have measured ...

Cluster algebras were invented by Sergey Fomin and Andrei Zelevinsky at the beginning of the year 2000. Their motivations came from Lie theory and more precisely from the study of the so-called canonical bases in quantum groups and that of total positivity in algebraic groups. Since then, cluster algebras have been linked to many other subjects ranging from higher Teichmüller theory through dis...

severe allergic reactions during specific immunotherapy may occur in the treatment of hymenoptera sting allergy. the objective of the present study was to examine the characteristics of allergic reactions during specific immunotherapy in patients with allergy towards hymenoptera venom in the iranian population. a prospective study was performed using the clinical reports of 27 patients with ana...

the ability to discover services in mobile ad hoc network (manet) is a major prerequisite. cluster basedcross layer intelligent service discovery for manet (cbisd) is cluster based architecture, caching ofsemantic details of services and intelligent forwarding using network layer mechanisms. the cluster basedarchitecture using semantic knowledge provides scalability and accuracy. also, the mini...

background: diabetes mellitus is one of the most important causes of morbidity and mortality all over the world. chronic high blood glucose is the root cause of developing future micro and macro vascular complications. in current study, we analyzed poorly controlled patients’ information by clustering method in order to find more homogenous sub-groups of patients for planning for further interv...

in this paper, an anomaly detection method in cluster-based mobile ad hoc networks with ad hoc on demand distance vector (aodv) routing protocol is proposed. in the method, the required features for describing the normal behavior of aodv are defined via step by step analysis of aodv and independent of any attack. in order to learn the normal behavior of aodv, a fuzzy averaging method is used fo...